These results can be understood within the framework of dissipative
galaxy formation
(Larson 1974,
1975,
Silk & Norman 1981,
Carlberg 1984a,
b,
Arimoto & Yoshii
1987,
Yoshii & Arimoto
1987,
Matteucci &
Tornambe 1987).
Carlberg's models in particular avoid some technical
limitations of Larson's pioneering work and make more detailed
predictions. In these models, the removal of enriched gas by
supernova-driven galactic winds is more efficient for less massive
galaxies (see also: Section 8.1). In
this spirit, the color-luminosity
relation is recast as a metallicity-escape velocity relation by
Vigroux et al. (1981):
ZVe0.9. Similarly, colors
and metallicities
correlate better with central velocity dispersions than with luminosities.
Carlberg (1984b)
also predicts the existence of a
second parameter in the Faber-Jackson and mass-metallicity
relations. Larson and Carlberg both predict that color and metallicity
gradients should-be stronger in more massive galaxies. Finally, they
make testable predictions about the relative shapes of isophotes and
isochromes (i.e. isometallicity contours). In Larson's models,
isochromes are considerably flatter than isophotes. However, Larson's
ellipticals are supported by rotation, which we now know is incorrect
(e.g.
Illingworth 1981,
Davies et al. 1983).
Carlberg's models are
generally supported by velocity anisotropy; then isochromes are only
slightly flatter than isophotes.

CCD photometry has provided high-quality measurements of color
gradients for large numbers of galaxies.
Boroson et al. (1983),
Davis et al. (1985),
Cohen (1986),
Boroson & Thompson
(1987),
and Bender &
Möllenhoff (1987)
present data on relatively small samples of
ellipticals, mostly in the Virgo cluster. They conclude that color
gradients are common in ellipticals. In the absence of nonthermal
emission or recent star formation, colors always get redder toward the
center. Interestingly, isophotes and isochromes generally have the
same shape. In fact, isochromes are occasionally rounder than
isophotes
(Boroson et al. 1983).
This is consistent with Carlberg's but not Larson's models.

The interpretation of color gradients in terms of stellar population
gradients has been discussed recently by
Efstathiou & Gorgas
(1985),
Gorgas & Efstathiou
(1987),
Davies & Sadler
(1987),
Couture & Hardy
(1988),
and references therein. They present extensive evidence for
gradients in Mg2 indices. Assuming the somewhat uncertain
conversions between Mg2 index and metallicity
(Terlevich et al. 1981)
and between color and metallicity
(Strom et al. 1976,
1978,
Tinsley 1978),
they find that the Mg2 and color gradients are mutually
consistent and imply typical changes of
[Fe / H] ~ -
0.2 per decade in radius. In excellent papers,
Baum et al. (1986) and
Thomsen & Baum
(1987,
1988)
derive metallicity gradients from narrowband surface photometry. They
also find that isochromes are not flatter than isophotes, in agreement
with spectroscopic results. Similar photometric measurements of the
Mg2 index are reported by
Vigroux et al. (1988).
Also,
Vader et al. (1988)
find that Mg2 gradients correlate well with broadband color
gradients. Further constraints are obtained by Peletier and coworkers
(Peletier et al. 1987,
1988a,
b,
c,
Peletier &
Valentijn 1988,
Peletier 1988).
They show that observed optical and near-infrared (JHK) color
gradients are mutually consistent (i.e. one can be derived from the
other using the separate optical and infrared color-luminosity
relations). All this suggests that the same change in stellar
population produces both the color-luminosity relation and the color
gradients. Using the new Yale isochrones
(Green et al. 1987),
Peletier and coworkers conclude that most color variations and gradients are
due to changes in metallicity. In typical ellipticals, these do not
exceed a factor of 10 inside re. However, age
gradients may be
present as well; the fraction of young stars may increase at larger radii.

Large data sets are needed to investigate correlations of color
gradients with other galaxy properties. The measurements are difficult
because color gradients are weak and because differential magnitude
measurements are sensitive to systematic errors. Nevertheless,
important data for early-type galaxies have been obtained by
Jedrzejewski (1987b),
Vigroux et al. (1988),
Franx (1988),
Franx et al. (1988),
and Peletier and collaborators (see above).

Vader et al. (1988)
analyze data from
Vigroux et al. (1988)
and obtain several interesting results. Whereas inward reddening is the
rule in elliptical galaxies and bulges, they find that dSph galaxies
tend to become bluer toward the center. Particularly interesting is
the observation that color gradients are correlated with the rotation
parameter
(V / )*:
Anisotropic, pressure-supported ellipticals have
smaller color gradients. We find the same effect, although with more
scatter, in the Franx and Peletier et al. data
(Figure 4).

The bright ellipticals in the
Franx (1988)
sample show weak
correlations of color gradients with luminosity, velocity dispersion,
integrated color, and Mg2 index: Weaker gradients are seen in
brighter, hotter, redder, and more metal-rich galaxies.
Gorgas & Efstathiou
(1987)
also find a marginally significant anticorrelation
between Mg2 gradients and velocity dispersion. However,
Peletier et al. (1988a)
find no significant correlations with the above
quantities; When we combine the Vader et al., Franx, and Peletier et
al. samples (Figure 4), color gradients in E and
SO galaxies are weak or absent at low luminosities (MB
> - 20) and largest near the peak of the luminosity function
(MB ~ - 20). The scatter exceeds the
measurement errors at all luminosities.

We also find a marginal correlation of color gradients with isophote
shapes (Figure 4). Color gradients in boxy
ellipticals get smaller as
boxyness increases [i.e. as a(4) / a decreases further
below 0]. There
are not enough data to look for variations of color gradients in disky
ellipticals.

Figure 4. Correlations of color gradients
with other galaxy properties. The gradients are defined as
(Color) /
(log r), in
magnitudes per
decade in radius; positive values indicate reddening toward the
center. The data are from
Vader et al. (1988;
circles),
Franx (1988;
squares), and Peletier et al.
(1988a;
triangles). The left panel shows
the dependence of color gradients on luminosity for dSph galaxies
(open circles) and for ellipticals and SOs (solid
symbols). Ellipticals become redder toward the center, but most dSph
galaxies have inverse gradients. The top-right panel shows the
relation between color gradients and the level of rotational support;
(V / )* =
1 for an isotropic oblate rotator. Anisotropic galaxies tend
to have smaller gradients. The bottom-right panel shows the
correlation with isophote shape (measured by B + 88). More boxy
galaxies [a(4) / a < 0] tend to have smaller color
gradients. Similar
trends are obtained using (U - R) color measurements.

These results are very preliminary. However, the trends are probably
real: All of the parameters are measured independently, and
measurement errors only diminish the correlations. If confirmed, these
correlations will provide important new information about galaxy
formation.

The absence of a strong correlation between the strengths of color
gradients and L or
is contrary to the predictions of the Larson and
Carlberg models. However, these do not include the effects of
postcollapse mergers, which are important at least for bright
ellipticals. The observations suggest that the properties of
early-type galaxies are determined by dissipative collapse and then
modified by mergers
(Vader et al. 1988).
Dissipative formation could
produce a mass-metallicity relation and metallicity gradients, which
are then gradually erased by mergers. The trend with luminosity at
MB
- 21 would then be a fossil of the initial correlation predicted by
Larson and Carlberg. Mergers may also produce correlated changes in
(V / )*
and a(4) / a (cf.
Figure 3). Normal color gradients
are not produced in diffuse dwarfs because of galactic winds
(Vader 1986a,
Dekel & Silk 1986);
their inverse color gradients could be due to recent star formation.

Finally, we discuss color gradients in cooling-flow galaxies. The
existence of cooling flows in ellipticals and cluster cores is
reasonably well established (e.g.
Fabian 1988).
Mass flow rates are uncertain, but
~ 1 - 1000
M
yr-1 are believed to be deposited inside a
few re, with a strong dependence on radius. The most
plausible fate of
the gas is star formation. Unless the initial mass function (IMF) is
strongly biased toward low-mass stars, observable color gradients
should result
(Sarazin &
O'Connell 1983,
Silk et al. 1986,
O'Connell 1988).
Blueing toward the centers of some
high- cooling-flow
galaxies is seen and interpreted as evidence for age gradients (e.g.
Wirth et al. 1983,
Romanishin 1986a,
1987,
Maccagni et al. 1988).
However, the extreme gradients reported by
Valentijn (1983) and
Valentijn &
Moorwood (1985)
are not confirmed by subsequent
work. A detailed comparison of color gradients in normal and
cooling-flow galaxies could provide strong constraints on the fate of
gas in cooling flows.